Structure-guided image measurement method

ABSTRACT

Structure-guided image estimation and measurement methods are described for computer vision applications. Results of the structure-guided estimation are symbolic representations of geometry entities such as lines, points, arcs and circles. The symbolic representation facilitates sub-pixel measurements by increasing the number of pixels used in the matching of image features to structural entities, improving the detection of structural entities within the image, weighting the contribution of each image sample to the measurement that is being made and optimizing that contribution. 
     After the structure-guided estimation, geometric entities are represented by their symbolic representations. Structure-guided measurements can be conducted using the symbolic representation of the geometric entities. Measurements performed from the symbolic representation are not limited by image resolution or pixel quantization error and therefore can yield sub-pixel accuracy and repeatability.

U.S. PATENT REFERENCES

1. U.S. Pat. No. 5,315,700 entitled, “Method and Apparatus for RapidlyProcessing Data Sequences”, by Johnston et. al., May 24, 1994.

2. U.S. Pat. No. 6,130,967 entitled, “Method and Apparatus for a ReducedInstruction Set Architecture for Multidimensional Image Processing”, byShih-Jong J. Lee, et. al., Oct. 10, 2000.

3. Pending Application Ser. No. 08/888,116 entitled, “Method andApparatus for Semiconductor Wafer and LCD Inspection UsingMultidimensional Image Decomposition and Synthesis”, by Shih-Jong J.Lee, et. al., filed Jul. 3, 1997.

4. U.S. Pat. No. 6,122,397 entitled, “Method and Apparatus for MasklessSemiconductor and Liquid Crystal Display Inspection”, by Shih-Jong J.Lee, et. al., Sep. 19, 2000.

5. U.S. Pat. No. 6,148,099 entitled, “Method and Apparatus forIncremental Concurrent Learning in Automatic Semiconductor Wafer andLiquid Crystal Display Defect Classification”, by Shih-Jong J. Lee et.al., Nov. 14, 2000.

CO-PENDING U.S. PATENT APPLICATIONS

1. U.S. patent application Ser. No. 09/693723, “Image Processing Systemwith Enhanced Processing and Memory Management”, by Shih-Jong J. Lee et.al, filed Oct. 20, 2000.

2. U.S. patent application Ser. No. 09/693378, “Image ProcessingApparatus Using a Cascade of Poly-Point Operations”, by Shih-Jong J.Lee, filed Oct. 20, 2000.

3. U.S. patent application Ser. No. 09/692948, “High Speed ImageProcessing Apparatus Using a Cascade of Elongated Filters Programmed ina Computer”, by Shih-Jong J. Lee et. al., filed Oct. 20, 2000.

4. U.S. patent application Ser. No. 09/703018, “Automatic Referencingfor Computer Vision Applications”, by Shih-Jong J. Lee et. al, filedOct. 31, 2000.

5. U.S. patent application Ser. No. 09/702629, “Run-Length Based ImageProcessing Programmed in a Computer”, by Shih-Jong J. Lee, filed Oct.31, 2000.

6. U.S. Patent Application entitled, “Structure-guided Image Processingand Image Feature Enhancement” by Shih-Jong J. Lee, filed Dec. 15, 2000.

REFERENCES

1. Draper N R and Smith H, “Applied Regression Analysis”, John Wiley &Sons, Inc., 1966, PP. 7-13.

2. Duda, R O and Hart P E, “Pattern Classification and Scene Analysis,”John Wiley and Sons, New York, 1973, PP. 332-335.

3. Haralick R M and Shapiro, L G, “Survey Image SegmentationTechniques,” Comput. Vision, Graphics Image Processing, vol. 29:100-132, 1985.

4. Silver, B, “Geometric Pattern Matching for General-Purpose Inspectionin Industrial Machine Vision”, Intelligent Vision '99 Conference—June28-29, 1999.

TECHNICAL FIELD

This invention relates to high accuracy image processing, specificallyto an improved method for measuring objects in an image with sub-pixelaccuracy and repeatability.

BACKGROUND OF THE INVENTION

Many computer vision applications require accurate and robustmeasurements of image features to detect defects or gather processstatistics. The capability of a computer vision system is oftencharacterized by its detection/measurement accuracy, repeatability andthroughput. It is desirable to achieve sub-pixel measurement accuracyand repeatability for many computer vision applications.

Application domain knowledge is available in most computer visionapplications. The application domain knowledge can often be expressed asstructures of image features such as edges, lines and regions. Thestructures include spatial relationships of object features such asshape, size, intensity distribution, parallelism, co-linearity,adjacency, etc. The structure information can be well defined inindustrial applications such as semiconductor, electronic or machinepart inspections. In machine part inspections, most of the work-pieceshave available Computer Aided Design (CAD) data that specifies itscomponents as entities (LINE, POINT, 3DFACE, 3DPOLYLINE, 3DVERTEX, LINE,POINT, 3DFACE, 3DPOLYLINE, 3DVERTEX, etc.) and blocks of entities. Inbiomedical or scientific applications, structure information can oftenbe loosely defined. For example, a cell nucleus is round and differentshapes can differentiate different types of blood cells or chromosomes.

Application domain knowledge can significantly improve the measurementcapability of a computer vision system. However, it is non-trivial toefficiently use the application domain knowledge in high precisionapplications that require sub-pixel accuracy, repeatability andreal-time throughput.

PRIOR ART

An image segmentation approach is used in the prior art for imagefeature detection or measurement. The image segmentation approachconverts a grayscale image into a binary image that contains object ofinterest masks. Binary thresholding is a common technique in the imagesegmentation approach (Haralick R M and Shapiro, L G, “Survey ImageSegmentation Techniques,” Comput. Vision, Graphics Image Processing,vol. 29: 100-132, 1985).

Image features such as edges in an image are smeared over a distance offour or five pixels, an effect that is the result of a reasonablysufficient sampling basis, imperfections in the camera optics, and theinevitability of physical laws (finite point spread function). Becauseedges or features of an image are imaged by the optical and imagingsystem as continuously varying gray levels, there exists no single graylevel that represents edge pixels. For this reason, any system thatdepends on segmentation or a binary thresholding of the image beforecritical dimensions are determined must necessarily introducequantization errors into the measurement. Binary thresholding alsoexacerbates the resolution limiting effect of system noise. Pixels whosegray levels are close to the threshold level are maximally affected bysmall variations due to additive noise. They may either be included orexcluded into the mask based on the noise contribution to theirinstantaneous value. These pixels are frequently located on theperiphery of the part, or a substructure of the part, where they havemaximal disruption of the derived measurement values.

Prior art (Silver, B, “Geometric Pattern Matching for General-PurposeInspection in Industrial Machine Vision”, Intelligent Vision '99Conference—Jun. 28-29, 1999) applies application domain structureinformation using a template matching method. An image of the object tobe located (the template) is stored. The template is compared to similarsized regions of the image over a range of positions, with the positionof greatest match taken to be the position of the object andmeasurements are conducted between the detected positions. Templatematching does not provide sub-pixel accuracy and repeatability since theestimated positions lie in pixel grids that exhibit spatial quantizationerror due to limitations in pixel pitch. Furthermore, the templatematching approach is sensitive to variations such as orientation andsize differences between the image and the template. Even within a smallrange of size and orientation changes, the match value drops off rapidlyand the ability to locate and measure image features drops with it.

Prior art applies application domain structure information through aprojection/dispersion approach. The projection/dispersion approachintegrates (projects) image pixel values over a pre-defined direction inthe image. This can be done for binary image (projection) or grayscaleimage (dispersion) and results in a one-dimensional line of values. Theapplication domain structure information defines the projectiondirections. However, the prior art approach is sensitive to systemvariations such as rotation. Rotation effect could result in theintegration of pixel values along a wrong direction that is destructiveto sub-pixel accuracies. Furthermore, the projection approach cannoteffectively combine multiple two-dimensional (or more dimensions)structure information where features of interest are along differentdirections. Therefore, only a limited number of image pixels (n) areused for feature estimation or measurement. Measurement uncertainty isrelated to $\frac{1}{\sqrt{n}}.$

Smaller n results in bigger uncertainty or lower accuracy.

Certain pixels in image feature region are more indicative than others.However, the prior art approach does not take advantage of thisinformation. Projection treats edge pixels and region pixels with equalweight. Prior Art does not score the reliability of each measurement.Prior Art does not do additional processing to improve accuracy andrepeatability on less reliable measurements. This is difficult toaccomplish since most prior art measurements are done in an ad hocfashion.

OBJECTS AND ADVANTAGES

It is an object of this invention to provide sub-pixel image featureestimation and measurement by using structure-guided image processingtechniques. The results of the structure-guided estimation is symbolicrepresentation of geometry entities such as lines, points, arcs andcircles. The symbolic representation is not limited by image resolutionor pixel quantization error and therefore facilitates sub-pixelmeasurements. The image feature estimation is based on grayscale weightsrather than a binary (mask) image.

It is another object of the invention to conduct the estimation in atleast two dimensions to avoid error caused by one-dimensional projectionand to utilize gray scale processing based on the weighted image withinfeature transition regions.

A further object of the invention is to guide the image featureestimation by structure constraints defined from application domainknowledge to increase accuracy. Accuracy is increased by using structureconstraints to link multiple features for an integrated estimation thatutilizes a large number of pixels (large n). Large n reduces themeasurement error and increases measurement repeatability.

It is a still further object of the invention to score measurementreliability and guided by the scores, improve accuracy and repeatabilityusing an iterative estimation approach.

It is an object of this invention to allow learning to determine theimportance and stability of image pixels and weight important and stablepixels higher in the estimation process.

SUMMARY OF THE INVENTION

This invention provides sub-pixel, high performance image basedestimation and measurement through a structure-guided image processingmethod. In the preferred embodiment, this invention performs twodimensional geometry estimation using images of grayscale weights foreach connected component in the measurement mask. The features fromwhich the masks and the weights are derived are described in theco-pending U. S. Patent Application entitled, “Structure-guided ImageProcessing and Image Feature Enhancement” by Shih-Jong J. Lee, filedDec. 15, 2000 which is incorporated herein in its entirety.

Results of the structure-guided estimation are symbolic representationof geometry entities such as lines, points, arcs and circles. Thesymbolic representation facilitates sub-pixel measurements by increasingthe number of pixels used in the matching of image features tostructural entities, improving the detection of structural entitieswithin the image, weighting the contribution of each image sample to themeasurement that is being made and optimizing that contribution.

After the structure-guided estimation, geometric entities arerepresented by their symbolic representations. Structure-guidedmeasurements can be conducted using the symbolic representation ofgeometric entities. Measurements performed from the symbolicrepresentation are not limited by image resolution or pixel quantizationerror and therefore can yield sub-pixel accuracy and repeatability.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the processing flow of the structure-guided imagemeasurement system.

FIG. 2 shows an alternative processing flow of the structure-guidedimage measurement system.

FIG. 3 shows a simple example of the structure-guided estimation method.Three lines are parallel to each other and are equal distance apart. Thefourth line is perpendicular to the three lines.

FIG. 4 shows lines with known slope yet unknown intersection c_(m).

FIG. 5 shows lines that pass a given intersection point ( X₀, y₀).

FIG. 6 shows two parallel line groups with a given angle Θ between thegroups.

FIG. 7 shows a circle/circular arc with its center on a given line.

FIG. 8 shows circle(s)/circular arc(s) with a given center point.

FIG. 9 shows two circles and a circular arc with a given radius r.

FIG. 10 shows an iterative optimization procedure to estimate (x_(cm),y_(cm)) and the same radius r.

FIG. 11 shows a circle and a circular arc with a given radius r andcenters on a given line.

FIG. 12 shows an iterative optimization procedure to estimate (x_(cm),y_(cm)) and the same radius r.

FIG. 13 shows a reference learning and robust weight generation process.

FIG. 14 illustrates one iteration of the robust estimation process.

FIG. 15 illustrates the intersection point between two non-parallellines.

FIG. 16 illustrates the angle between two non-parallel lines.

FIG. 17 illustrates distance between two non-parallel lines intersectedby a reference line.

FIG. 18 illustrates the distance between a point and a line.

FIG. 19 illustrates the distance between two parallel lines.

FIG. 20 illustrates the distance between two non-parallel lines at anequal angle intersection line passing a given point.

FIG. 21 illustrates intersection points between a line and a circle.

FIG. 22 illustrates intersection points between two circles.

FIG. 23 illustrates tangential lines of a circle and a given point.

DETAILED DESCRIPTION OF THE INVENTION

This description of a preferred embodiment of a structure-guided imagemeasurement method describes a set of detailed processes through whichan image processing system can achieve sub-pixel accuracy andrepeatability of image feature measurement. This invention performs twodimensional geometry estimation using images of grayscale weights foreach connected component in the measurement mask. The estimation isbased on grayscale weights rather than a binary image. The estimation isconducted in two dimensions to avoid error caused by one-dimensionalprojection. The estimation is guided by structure constraints definedfrom application domain knowledge to increase accuracy. It usesstructure constraints to link multiple features for an integratedestimation that utilizes a large number of points (large n). Large nreduces the measurement ambiguity. The results of the structure-guidedestimation are symbolic representation of geometry entities such aslines, points, arcs and circles. Alignment of the symbolic geometricentities with their respective image features facilitates robustsub-pixel measurements.

This invention can use learning to determine the stability of imagepixels and weigh stable pixels higher in the estimation process.Reliability of measurement is scored. Guided by the scores, accuracy andrepeatability is improved using iterative robust estimation.

I. Structure-guided Image Measurement System

FIG. 1 shows the processing flow of the structure-guided imagemeasurement system of this invention. As shown in FIG. 1, inputs to thestructure-guided image measurement system include measurement mask(s)100 and a measurement weight image 112. The structure-guided estimationmodule 102 performs estimation from the weight image 112 within theregions defined by each component of the measurement mask(s) 100.Application domain structure information 110 is encoded into constraintsfor the structure-guided estimation 102. The structure-guided estimationmodule creates symbolic representation 104 of geometric entities such aslines, points, arcs and circles. The structure-guided measurements 106are performed using the symbolic representation to achieve measurementresults 108 with sub-pixel accuracy.

The measurement mask(s) 204 and measurement weight image 216 can beautomatically generated from the input image 200 as shown in FIG. 2. Astructure-guided image processing and feature enhancement system thatextracts and enhances image features of interest and generatesmeasurement mask(s) and weights from the feature enhanced image isdisclosed in a co-pending U.S./Patent Application entitled,“Structure-guided Image Processing and Image Feature Enhancement” byShih-Jong J. Lee, filed Dec. 15, 2000 which is incorporated herein inits entirety.

II. Structure-guided Estimation

The structure-guided estimation method 206 performs estimation from theweight image 216 within the regions defined by each component of themeasurement mask(s) 204. The estimation is conducted by a weightedminimum-square-error (MSE) method. The estimation finds the parametersthat minimize a cost function. The cost function is defined as theweighted square error between the structural model (symbolicrepresentation) and all data points of all entities included in theestimation minus an additional structural constraint term. The entitiesare defined by each component of the measurement mask(s). Thecorresponding points in the measurement weight image weighs each datapoint during the estimation process.${Cost} = {{\sum\limits_{m \in M}\quad {\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {{Model\_ Error}\left( {x_{i},y_{i}} \right)} \right\rbrack}^{2}}} - {{Additional\_ structure}{\_ constraint}}}$

Where M is the set of all components in the measurement masks and C_(m)corresponds to the m-th component of the mask. Model_Error functionrepresents the difference between the structure representation and thereal data.

FIG. 3 illustrates a simple example of the structure-guided estimationmethod of this invention. There are four lines 300, 314, 312, 304 in theexample shown in FIG. 3. Each line has a boundary measurement mask 308that defines the regions to perform estimation using the pixel values inthe grayscale weight image 306 shown surrounding each line with a crosshatched pattern. In this figure, the darkest part of the line is shownin the approximate center and indicated by a darkened region. Thestructure constraints that are used to guide the estimation include aparallel constraint 316 for the three lines 300, 314, 312 on the left ofFIG. 3. In addition, an equal distance constraint 310 is also applied tothe distances between the adjacent parallel lines. The fourth line 304is included in the estimation process using an orthogonal constraint 302that requires that it is perpendicular to the parallel lines. Theoutputs 208 of the structure-guided estimation method of this inventionare the symbolic representation of the four lines. Therefore, theinformation embedded in the measurement masks and gray scale weightimages are transformed into the parameters of the symbolicrepresentation. Measurements performed from the symbolic representationare no longer limited by image resolution or pixel quantization errorand therefore can yield sub-pixel accuracy and repeatability. Thesymbolic representation can also be used with a computer graphic programto display the detected features.

II.1 Symbolic Representation of Geometric Entities

To achieve sub-pixel accuracy, the outputs of the structure-guidedestimation module are the symbolic representation of the geometricentities. In one embodiment of the invention, the entities include scalevalue, point, line, circle and region of interest or arrays (sets) ofvalues, points, lines, circles or regions of interest.

A scale value is represented by a real number. A point location isrepresented by two integers corresponding to its x and y imagecoordinates. A line position is represented by a line equation:

ax+by+c=0 with the constraint that a ² +b ²=1 and b≧0.

A circle is represented by a circle equation

x ² +y ² +ax+by+c=0.

The center of the circle is located at$\left( {{- \quad \frac{a}{2}},{- \quad \frac{b}{2}}} \right)$

and the radius of the circle is $\sqrt{\frac{a^{2} + b^{2}}{4} - c}.$

A rectangular region of interest is represented by its upper-left andlower-right corner points.

Those skilled in the art should recognize that the geometric entitiescould include other two dimensional curves such as ellipse, parabola,hyperbola, cubic and higher order polynomial functions, splinefunctions, etc. The region of interest could be generalized into closedpolygons. The image coordinates can be transformed into other coordinatesystems. Furthermore, the structure-guided estimation of this inventioncan be generalized to estimate three dimensional or higher dimensionalgeometric entities by correlating constraints among multiple images(such as stereo image pairs) and can also include such things as coloror motion or separate images joined by a known relation (such as anoutside image and an inside image).

II.2 Structure-guided Geometric Entity Estimation

The structure-guided estimation module estimates the parameters of thesymbolic representation of the geometric entities from the grayscaleweight image under the structure constraints. Different structureconstraints and combinations of the constraints can be used in theestimation processes. In one embodiment of the invention, constrainedweighted least squares estimation is used as the basis for theestimation. The estimation finds the parameters that minimize theweighted square error for all data points of all entities included inthe estimation. The corresponding point in the measurement weight imageweights each data point during the estimation process. The followingsections list some estimation methods in one preferred embodiment ofthis invention.

A. Structure-guided Line Estimation

A.1 Line Estimation Without Structure Constraints

When no structure constraint is available, the cost function for line mis${Cost}_{m} = {{\sum\limits_{i \in L_{m}}{w_{i}\left\lbrack {{a_{m}x_{i}} + {b_{m}y_{i}} + c_{m}} \right\rbrack}^{2}} - {\lambda \left( {a^{2} + b^{2} - 1} \right)}}$

Where L_(m) is the mask region defined for the estimation of line m.

A closed form solution exists for determining a_(m), b_(m) and c_(m)that minimize Cost_(m). (Draper N R and Smith H, “Applied RegressionAnalysis”, John Wiley & Sons, Inc., 1966, PP. 7-13)

A.2 Line Estimation Constrained by a Given Slope

The structure constraint requires all lines 416, 418, 406, 422 have asame slope that is known a priori as shown in FIG. 4. Each line has grayscale weights 400, 410, 412, 414 within a mask region as shown in 402,404, 420, 408. C_(m) is not known.

The given slope uniquely defines a and b of the line equations. The costfunction is defined as,${Cost} = {\sum\limits_{m \in L}\quad {\sum\limits_{i \in L_{m}}{w_{i}\left\lbrack {{a\quad x_{i}} + {b\quad y_{i}} + c_{m}} \right\rbrack}^{2}}}$

Where L is the set of lines included in the estimation masks; L_(m) isthe mask region defined for line m. A closed form solution exists fordetermining c_(m) that minimizes Cost.

A.3 Line Estimation Constrained by a Given Intersection Point

The structure constraint requires all lines to pass one givenintersection point (X₀, Y₀) as shown in FIG. 5. In FIG. 5 the commonpoint of intersection 502 is shown wherein the lines 514, 510, 506intersect. Each line has grayscale weights 516, 520, 522 within maskregion 504, 508, 512.

The cost function is${Cost} = {\sum\limits_{m \in L}\left( \quad {{\sum\limits_{i \in L_{m}}{w_{i}\left\lbrack {{{a\quad}_{m}\left( {x_{i} - x_{0}} \right)} + {b_{m}\quad \left( {y_{i} - y_{0}} \right)}} \right\rbrack}^{2}} + {\lambda_{m}\left( {a_{m}^{2} + b_{m}^{2} - 1} \right)}} \right)}$

Where L is the set of lines included in the estimation masks; L_(m) isthe mask region defined for line m. A closed form solution exists fordetermining a_(m) and b_(m) for each line in L that minimize Cost.

A.4 Line Estimation Constrained by Parallelism and Orthogonal Relations

FIG. 3 shows an example of this case. The structure constraint includestwo groups of parallel lines L 300, 314, 312 and P 304. The lines in Land the lines in P are perpendicular to each other as shown in FIG. 3.The cost function is $\begin{matrix}{{Cost} = \quad {{\sum\limits_{m \in L}\quad {\sum\limits_{i \in L_{m}}{w_{i}\left\lbrack {{a\quad x_{i}} + {b\quad y_{i}} + c_{m}} \right\rbrack}^{2}}} +}} \\{\quad {{\sum\limits_{n \in P}\quad {\sum\limits_{i \in P_{n}}{w_{i}\left\lbrack {{b\quad x_{i}} - {a\quad y_{i}} + c_{n}} \right\rbrack}^{2}}} - {\lambda \left( {a^{2} + b^{2} - 1} \right)}}}\end{matrix}$

A closed form solution exists for determining a, b, c_(m) and c_(n) thatminimize Cost. When P is an empty set, only a parallel line constraintexists for a set of lines. This is a degenerate form of the structureconstraint in this more general case. When only one line each existed ingroups L and P, the constraint becomes the existence of two orthogonallines. This is a degenerate form of the structure constraint in thismore general case.

A.5 Line Estimation Constrained by Parallelism and Equal DistanceRelations

FIG. 3 shows an example of this case. There is a group of parallel linesL 300, 314, 312 with a common slope corresponding to unknown values aand b. The lines in L can be sequentially ordered from 0 to K by theirproximity to each other with the adjacent lines a fixed but unknowndistance d apart 310. The cost function is${Cost} = {{\sum\limits_{m \in L}\quad {\sum\limits_{i \in L_{m}}{w_{i}\left\lbrack {{a\quad x_{i}} + {b\quad y_{i}} + {m\quad d} + c_{0}} \right\rbrack}^{2}}} - {\lambda \left( {a^{2} + b^{2} - 1} \right)}}$

A closed form solution exists for determining a, b, d and c₀ thatminimize Cost.

A.6 Line Estimation Constrained by Parallelism and a Given AngleRelation

The structure constraint includes two groups of parallel lines L 600,602, 614, 604 and P 612, 610, 608, 606. The lines in L and the lines inP are intersected with a given angle Θ 618, 616 as shown in FIG. 6.

The cost function is $\begin{matrix}{{Cost} = \quad {{\sum\limits_{m \in L}\quad {\sum\limits_{i \in L_{m}}{w_{i}\left\lbrack {{a\quad x_{i}} + {b\quad y_{i}} + c_{m}} \right\rbrack}^{2}}} +}} \\{\quad {{\sum\limits_{n \in P}\quad {\sum\limits_{i \in P_{n}}{w_{i}\left\lbrack {{c\quad x_{i}} + {d\quad y_{i}} + c_{n}} \right\rbrack}^{2}}} - {\lambda_{1}\left( {{a\quad c} + {b\quad d} - {\cos \quad \Theta}} \right)} -}} \\{\quad {{\lambda_{2}\left( {a^{2} + b^{2} - 1} \right)} - {\lambda_{3}\left( {c^{2} + d^{2} - 1} \right)}}}\end{matrix}$

An iterative optimization method can be used to determine a, b, c_(m)and c, d, c_(n) that minimizes Cost.

When only one line each exists in groups L and P, the constraint becomestwo lines with an intersection angle Θ. This is a degenerate form ofthis more general structure constraint.

B. Structure-guided Circle/Circular Arc Estimation

B.1 Circle/Circular Arc Estimation Without Structure Constraints

When no structure constraint is available, the cost function forcircle/circular arc m is${Cost}_{m} = {\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i}^{2} + \quad y_{i}^{2}} \right) + {a_{m}\quad x_{i}} + {{b\quad}_{m}y_{i}} + c_{m}} \right\rbrack}^{2}}$

Where C_(m) is the mask region defined for circle/circular arc m.

A closed form solution exists for determining a_(m), b_(m) and c_(m)that minimize Cost_(m). The center of the circle/circular arc m islocated at $\left( {{- \frac{a_{m}}{2}},{- \frac{b_{m}}{2}}} \right)$

and its radius is $\sqrt{\frac{a_{m}^{2} + b_{m}^{2}}{4} - c_{m}}.$

B.2 Circle/Circular Arc Estimation Constrained by Center on a Given Line

The structure constraint requires that the center of the circle/circulararc is on a given line

dx+ey+f=0

This case is shown in FIG. 7. In FIG. 7, a line 700 passes the center704 of a circle 706. The circle 706 has a circular arc 702. The costfunction for the circle/circular arc m is${Cost}_{m} = {{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i}^{2} + \quad y_{i}^{2}} \right) + {a_{m}\quad x_{i}} + {{b\quad}_{m}y_{i}} + c_{m}} \right\rbrack}^{2}} - {\lambda \left( {{a_{m}d} + {b_{m}e} - {2f}} \right)}}$

A closed form solution exists for determining a_(m), b_(m) and c_(m)that minimize Cost_(m). The center of the circle/circular arc m islocated at $\left( {{- \frac{a_{m}}{2}},{- \frac{b_{m}}{2}}} \right)$

and its radius is $\sqrt{\frac{a_{m}^{2} + b_{m}^{2}}{4} - c_{m}}.$

B.3 Circle(s)/Circular Arc(s) Estimation Constrained by a Given CenterPoint

The structure constraint gives a fixed center location 804 for thecircle(s) 800, 806/circular arc(s) 802 at (x_(c), y_(c)). The estimateis to find radius r_(m) for each circle/circular arc C_(m) in the set ofcircle(s)/circular arc(s) included in the estimation masks. Thisstructure is shown in FIG. 8.

The cost function is${Cost} = {\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{c}} \right)^{2} + \left( {y_{i} - \quad y_{c}} \right)^{2} - r_{m}} \right\rbrack}^{2}}}$

Where C is the set of circle(s)/circular arc(s) included in theestimation masks. A closed form solution exists for determining r_(m)for all mεC that minimize Cost.

B.4 Circle(s)/Circular Arc(s) Estimation Constrained by the Same CenterPoint

The structure constraint requires that all circle(s)/circular arc(s)have a common unknown center point. This structure is similar to thatshown in FIG. 8 with the exception that the common center position isunknown.

The cost function is${Cost} = {\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack \left( {x_{i}^{2} + \quad y_{i}^{2} + {a\quad x_{i}} + {b\quad y_{i}} + c_{m}} \right\rbrack^{2} \right.}}}$

A closed form solution exists for determining a, b and c_(m) for all mεCthat minimize Cost.

B.5 Circle(s)/Circular Arc(s) Estimation Constrained by a Given Radius

The structure constraint gives a fixed radius value r 902, 912, 904 forthe circle(s) 900, 908/circular arc(s) 906 being estimated. Thestructure is shown in FIG. 9.

The estimate is to find centers (x_(cm), y_(cm)) for eachcircle/circular arc C_(m) in the set of circle(s)/circular arc(s), C,included in the estimation masks.

The cost function is${Cost} = {\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} - r^{2}} \right\rbrack}^{2}}}$

In one embodiment of the invention, an iterative optimization approachsuch as Newton-Rapson method is used to determine (x_(cm), y_(cm)) foreach circle/circular arc C_(m) in the set of circle(s)/circular arc(s)that minimize Cost.

B.6 Circle(s)/Circular Arc(s) Estimation Constrained by Same Radius

The structure constraint requires that all circle(s)/circular arc(s)have the same yet unknown radius r. This structure is similar to that isshown in FIG. 9 with the exception that the common radius is unknown.

The cost function is${Cost} = {\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} - d} \right\rbrack}^{2}}}$

Where d=r².

In one embodiment of the invention, an iterative optimization procedureis used to determine r and (x_(cm), y_(cm)) for each circle/circular arcC_(m) in the set of circle(s)/circular arc(s) that minimize Cost. Theiterative optimization procedure is shown in FIG. 10. It starts with aninitial estimate 1000 without any constraint and then estimates r given(x_(cm), y_(cm)) 1002. This can be done using the method in section B.3.It then updates the estimate of (x_(cm), y_(cm)) given r 1004 estimatedfrom the previous step 1002. This can be done using the method insection B.5. The r and (x_(cm), y_(cm)) estimation procedures can berepeated until the values converge 1006 and the process is completed1008.

B.7 Circle(s)/Circular Arc(s) Estimation Constrained by a Given Radiusand Centers on a Given Line

The structure constraint gives a known radius value r 1102, 1110 for thecircle(s) 1104, 1108/circular arc(s) 1106 included for the estimation.It also requires that the centers of the circle(s)/circular arc(s) 1112,1114 are located on a given line 1100

dx+ey+f=0

The structure is illustrated in FIG. 11.

The cost function is $\begin{matrix}{{Cost} = \quad {{\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} - r^{2}} \right\rbrack}^{2}}} -}} \\{\quad {\sum\limits_{c_{m} \in C}{\lambda_{m}\left( {{d\quad x_{cm}} + {e\quad y_{cm}} + f} \right)}}}\end{matrix}$

In one embodiment of the invention, an iterative optimization approachsuch as Newton-Rapson method is used to determine (x_(cm), y_(cm)) foreach circle/circular arc C_(m) in the set of circle(s)/circular arc(s)that minimize Cost.

B.8 Circle(s)/Circular Arc(s) Estimation Constrained by a Same Radiusand Centers on a Given Line

The structure constraint requires a same yet unknown radius value r forthe circle(s)/circular arc(s) included for the estimation. It alsorequires that the centers of the circle(s)/circular arc(s) are locatedon a given line

dx+ey+f=0

This structure is similar to that is shown in FIG. 11 with the exceptionthat the common radius is unknown.

The cost function is $\begin{matrix}{{Cost} = \quad {{\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} - d} \right\rbrack}^{2}}} -}} \\{\quad {\sum\limits_{c_{m} \in C}{\lambda_{m}\left( {{d\quad x_{cm}} + {e\quad y_{cm}} + f} \right)}}}\end{matrix}$

Where d=r².

In one embodiment of the invention, an iterative optimization procedureis used to determine r and (x_(cm), y_(cm)) for each circle/circular arcC_(m) in the set of circle(s)/circular arc(s) that minimize Cost. Theiterative optimization procedure is shown in FIG. 12. It starts with aninitial estimate 1200 without any constraint and then estimates r giventhe initial estimate of (x_(cm), y_(cm)) 1202. There is a closed formsolution for this estimate. It then derives a new d=r² and updates theestimate of (x_(cm), y_(cm)) given d 1204. This can be done using themethod in section B.7. The r and (x_(cm), y_(cm)) estimate proceduresare repeated until the values converge 1206 and the procedure iscompleted 1208.

B.9 Circle(s)/Circular Arc(s) Estimation Constrained by a GivenTangential Line

The structure constraint gives a known tangential line dx+ey+f=0 1116,1118 for the circle(s)/circular arc(s) included for the estimation. Thestructure is illustrated in FIG. 11.

The cost function is${Cost} = {\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} - \left( {{d\quad x_{cm}} + {e\quad y_{cm}} + f} \right)^{2}} \right\rbrack}^{2}}}$

In one embodiment of the invention, an iterative optimization approachsuch as Newton-Rapson method is used to determine (x_(cm), y_(cm)) foreach circle/circular arc C_(m) in the set of circle(s)/circular arc(s)that minimize Cost.

B.10 Circle(s)/Circular Arc(s) Estimation Constrained by a GivenTangential line and a Given Radius

The structure constraint requires a known tangential line 1116, 1118dx+ey+f=0 and the radius r 1102, 1110. The structure is illustrated inFIG. 11.

The cost function is $\begin{matrix}{{Cost} = \quad {{\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} - r} \right\rbrack}^{2}}} -}} \\{\quad {\sum\limits_{c_{m} \in C}\left\lbrack {{\lambda_{m}\left( {{d\quad x_{cm}} + {e\quad y_{cm}} + f} \right)}^{2} - r^{2}} \right\rbrack}}\end{matrix}$

In one embodiment of the invention, an iterative optimization approachsuch as Newton-Rapson method is used to determine (x_(cm), y_(cm)) foreach circle/circular arc C_(m) in the set of circle(s)/circular arc(s)that minimize Cost.

B.11 Circle(s)/Circular Arc(s) Estimation Constrained by a GivenTangential line and a Center Lies in a Line

The structure constraint gives a known tangential line 1116, 1118

dx+ey+f=0

and the center pass through the line 1100 px+qy+r=0 for thecircle(s)/circular arc(s) included for the estimation. The structure isillustrated in FIG. 11.

The cost function is $\begin{matrix}{{Cost} = \quad {\sum\limits_{c_{m} \in C}{\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {\left( {x_{i} - \quad x_{cm}} \right)^{2} + \left( {y_{i} - \quad y_{c\quad m}} \right)^{2} -} \right.}}}} \\{\left. \quad \left( {{d\quad x_{cm}} + {e\quad y_{cm}} + f} \right)^{2} \right\rbrack^{2} - {\sum\limits_{c_{m} \in C}{\lambda_{m}\left( {{p\quad x_{cm}} + {q\quad y_{cm}} + r} \right)}}}\end{matrix}$

In one embodiment of the invention, an iterative optimization approachsuch as Newton-Rapson method is used to determine (x_(cm), y_(cm)) foreach circle/circular arc C_(m) in the set of circle(s)/circular arc(s)that minimize Cost.

B.12 Circle(s)/Circular Arc(s) Estimation Constrained by GivenTangential Lines

The structure constraint gives two known tangential lines 1117, 1116

dx+ey+f=0

px+qy+r=0

for the circle 1104 included for the estimation. The structure isillustrated in FIG. 11. There are two steps to performing theestimation. Firstly, from two lines, we can calculate the middle line,and then using the method of B.11, Circle(s)/Circular Arc(s) EstimationConstrained by a Given Tangential line and a Center lies in a line.

Those skilled in the art should recognize that the estimation method ofthis invention can include other two dimensional curves such as ellipse,parabola, hyperbola, cubic and higher order polynomial functions, splinefunctions, etc. Pre-processing such as orthogonal, perspective or otherprojections can be conducted to transform from other coordinate systemsto the image coordinate before the estimation. Furthermore, thestructure-guided estimation of this invention can be generalized toestimate three dimensional or higher dimensional geometric entities bycorrelation of constraints among multiple images. Other types of costfunction and estimation method can also be applied. For example,eigenvector fit rather than MSE fit can be used for estimation (Duda, RO and Hart P E, “Pattern Classification and Scene Analysis,” John Wileyand Sons, New York, 1973, PP. 332-335.)

II.3 Robust Estimation

The structure-guided estimation uses structure constraints to resolveambiguity and allows the use of more pixels (large n) for eachestimation parameter. The estimation is based on two-dimensional weightsthat are derived from the image feature magnitude. Certain pixels inimage feature region are more stable or contribute more to the resultthan others. The structure-guided estimation of this invention canimprove the estimation robustness through automatic learning. As shownin FIG. 13, a reference learning process 1310 generates referenceweights 1308 from the learning images 1300. The reference learningprocess disclosed in co-pending U.S. patent application Ser. No.09/703018, “Automatic Referencing for Computer Vision Applications”, byShih-Jong J. Lee et. al, filed Oct. 31, 2000 which is incorporated inits entirety herein is used in one embodiment of the invention. Thereference weights 1308 and the measured weights 1304 can be combined toform a robust weight image 1306 for estimation. In one embodiment of theinvention, the combination is accomplished by a weighted average of thetwo images as follows:

I _(robust weight)(x _(i) , y _(i))=α(x _(i) , y _(i))I_(measured weight)(x _(i) , y _(i))+(1.0−α(x _(i) , y _(i)))I_(reference weight)(x _(i) , y _(i))

Other combination methods such as maximum, minimum, multiplication, etc.of the two images can be used according to the characteristics for theparticular application.

Methods for using reference images are described in co-pending U.S.patent application Ser. No. 09/703018, “Automatic Referencing forComputer Vision Applications”, by Shih-Jong J. Lee et. al, filed Oct.31, 2000 incorporated herein in its entirety. In another embodiment ofthe invention, a reference weight deviation image is generated and thedeviation image is used to normalize the measured weights by an imagedivision that can be implemented by a Look up Table:

I _(robust weight)(x _(i) , y _(i))=(α(x _(i) , y _(i))I_(measured weight)(x _(i), y_(i))+(1.0−α(x _(i) , y _(i)))I_(reference weight)(x _(i) , y _(i)))/I _(reference deviation)(x _(i) ,y _(i))

Co-pending U.S. patent application Ser. No. 09/693723 entitled, “ImageProcessing System with Enhanced Processing and Memory Management”, byShih-Jong J. Lee et. al, filed Oct. 20, 2000 which is incorporated inits entirety herein describes Look Up Table methodology. In thestructure-guided estimation process, the difference between theestimated geometric entities and the weight images can be used togenerate scores that indicate the reliability of each point in theestimation mask. Guided by the scores, accuracy and repeatability can befurther improved by a robust estimation method. FIG. 14 illustrates anexample of the robust estimation process. FIG. 14(a) 1400 is the initialweight data within the estimation mask. FIG. 14(b) shows the initialestimation result 1412 superimposed on the original weight data 1414.Based on the initial estimation result, reliability scores aregenerated. In one embodiment of the invention, the reliability score fora point i can be derived as follows:${Score}_{i} = \frac{w_{i}*{Model\_ Error}\left( {x_{i},y_{i}} \right)^{2}*{\sum\limits_{m \in M}\quad {\sum\limits_{i \in C_{m}}1}}}{\sum\limits_{m \in M}\quad {\sum\limits_{i \in C_{m}}{w_{i}\left\lbrack {{Model\_ Error}\left( {x_{i},y_{i}} \right)} \right\rbrack}^{2}}}$

Using the reliability score, the weights can be updated to reduceweights for the lower score points. Reductions occur on weight datapoints 1406 and 1408 in the FIG. 14(c) example. A new estimation isperformed using the updated weights and a new estimation result isgenerated 1410. The reliability score guided weight adjustment andestimation process is repeated until the estimation result converges ora maximum number of iterations is exceeded.

III. Structure-guided Measurements

After the structure-guided estimation, geometric entities arerepresented by their symbolic representations. Structure-guidedmeasurements can be conducted using the symbolic representation ofgeometric entities. Measurements performed from the symbolicrepresentation are not limited by image resolution or pixel quantizationerror and therefore can yield sub-pixel accuracy and repeatability.

In one embodiment of the invention, the measurements can be achieved byapplying measurement rules to the estimated parameters of the symbolicrepresentation of geometric entities. The following sections describesome measurement rules in one preferred embodiment of the invention.

III.1 Intersection Point Between Two Non-parallel Lines:

The intersection point to be determined is illustrated in FIG. 15. Letthe two lines 1500, 1504 be represented as

a ₁ x+b ₁ y+c ₁=0

a ₂ x+b ₂ y+c ₂=0

The intersection point (x, y) 1502 between the two lines can bedetermined by the following rule:$x = \frac{{b_{1}c_{2}} - \quad {b_{2}c_{1}}}{{a_{1}b_{2}} - \quad {a_{2}b_{1}}}$$y = \frac{{a_{2}c_{1}} - \quad {a_{1}c_{2}}}{{a_{1}b_{2}} - \quad {a_{2}b_{1}}}$

III.2 Smallest Angle Between Two Non-parallel Lines:

The angle to be determined 1602 is illustrated in FIG. 16. Let the twolines 1600, 1604 be represented as

a ₁ x+b ₁ y+c ₁=0

a ₂ x+b ₂ y+c ₂=0

The smallest angle Θ between the two lines can be determined from thefollowing rule:$\Theta = {\cos^{- 1}\frac{{{a_{1}a_{2}} + {b_{1}b_{2}}}}{{\sqrt{a_{1}^{2} + b_{1}^{2}}\quad \sqrt{a_{2}^{2} + b_{2}^{2}}}\quad}}$

III.3 Distance Between Two Non-parallel Lines Intersected by a ReferenceLine:

The distance to be determined 1704 is illustrated in FIG. 17. Let thetwo lines 1700, 1706 be represented as

Line 1: a ₁ x+b ₁ y+c ₁=0

Line 2: a ₂ x+b ₂ y+c ₂=0,

and the reference line 1702 be represented by

 Line r: a _(r) x+b _(r) y+c _(r)=0

Let the intersection between line 1 and line r 1710 be (x₁, y₁) and theintersection between line 2 and line r 1708 be (x₂, y₂). The distance d1704 can be determined from the following rule:

d={square root over ((x ₂ −x ₁)²+(y ₂ −y ₁)²)}

III.4 Shortest Distance Between a Point and a Line:

The shortest distance 1804 between a point 1802 and a line 1800 isillustrated in FIG. 18.

Let the line be

ax+by+c=0

and the point be (x₀, y₀)

The shortest distance d between the point and the line is$d = \frac{{{a\quad x_{0}} + {b\quad y_{0}} + c}}{\sqrt{a^{2} + b^{2}}}$

III.5 Distance Between Two Parallel Lines:

The distance d 1904 between two parallel lines 1900, 1902 is illustratedin FIG. 19.

Let the two lines be

ax+by+c ₁=0 and

ax+by+c ₂=0.

The distance d between the two parallel lines is$d = \frac{{c_{1} - c_{2}}}{\sqrt{a^{2} + b^{2}}}$

III.6 Distance Between Two Non-parallel Lines at an Equal AngleIntersection Line Passing a Given Point:

The distance 2002 between two non-parallel lines 2000, 2008 at an equalangle 2012, 2004 intersection line 2006 passing a given point 2010 isillustrated in FIG. 20.

Let the two lines be

 Line 1: a ₁ x+b ₁ y+c ₁=0 and

Line 2: a ₂ x+b ₂ y+c ₂=0.

The given point 2010 is (x_(r), y_(r)) and the intersection line is

Line r: a(x−x _(r))+b(y−y _(r))=0

The equal angle constraint requiresa  a₁ + b  b₁ = a  a₂ + b  b₂.

With this constraint, the slope a and b of the intersection line can besolved using known parameters a₁, b₁, a₂, b₂, x_(r), y_(r).

The distance d between the two non-parallel lines can then be determinedwith the rules defined in section III.3.

III.7 Intersection Points Between a Line and a Circle:

The intersection points 2110, 2106, 2108 between a line 2100, 2102, 2104and a circle 2112 is illustrated in FIG. 21. Let the line representationbe

ax+by+c=0

and the circle representation be

(x−x _(c))²+(y−y _(c))² −r ²=0

Let

D=a _(x) _(c) +b _(y) _(c) +c

There are three cases:

Case 1: |D|>r

No intersection

Case 2: |D|=r

One intersection point at (x_(c)−aD, y_(c)−bD)

Case 3: |D|<r

Two intersection points at (x_(c)−aD+b{square root over (r²−D²)},y_(c)−bD−a{square root over (r²−D²)}) and (x_(c)−aD−b{square root over(r²−D²)}, y_(c)−bD+a{square root over (r²−D²)})

III.8 Intersection Points Between Two Circles:

The intersection points between two circles is illustrated in FIG. 22for three cases. Case 1 2200 is for non-intersection circles 2202 and2214; case 2 2206 involves two circles 2204, 2212 that have a singlepoint of intersection 2214; case 3 2210 involves two circles 2208, 2212having two points of intersection 2216, 2218.

Let the two circle representations be

(x−x ₁)²+(y−y ₁)² =r ₁ ²

(x−x ₂)²+(y−y ₂)² =r ₂ ²

The line passes through the intersection point(s) of the circles is

ax+by+c=0

Where

a=2(x ₂ −x ₁),

b=2(y ₂ −y ₁) and

c=x ₁ ² −x ₂ ² +y ₁ ² −y ₂ ² −r ₁ ² +r ₂ ²

The rule in III.7 can be applied to find the intersection points betweenax+by+c=0 and

(x−x ₁)²+(y−y ₁)² =r ₁ ²

III.9 Tangential Lines of a Circle and a Given Point:

The tangential lines of a circle and a given point is illustrated inFIG. 23. Case 1 2308 shows the situation where a tangential line doesnot exist. Case 2 shows line 2300 tangent to circle 2312 at a singlepoint 2310. Case 3 shows two lines 2306, 2304 tangent to circle 2312 attwo points with the two lines having an intersection at 2302

Let the circle representation be

(x−x _(c))²+(y−y _(c))² =r ₁ ²

the point be (x_(p), y_(p))

We define the tangential line as

a(x−x _(p))+b(y−y _(p))=0, a ² +b ²=1

D ²=(x _(c) −x _(p))²+(y _(c) −y _(p))²

Let

Case 1: D²<r²

Tangential line does not exist

Case 2: D²=r²

One tangential line exists and is defined as follows:$a = \frac{x_{c} - x_{p}}{r}$ $b = \frac{y_{c} - y_{p}}{r}$

Case 3: D²>r²

Two tangential lines exist. The first line is defined as follows:$a = \frac{{r\left( {x_{c} - x_{p}} \right)} + {\left( {y_{c} - y_{p}} \right)\quad \sqrt{D^{2} - r^{2}}}}{D^{2}}$$b = \frac{{r\left( {y_{c} - y_{p}} \right)} - {\left( {x_{c} - x_{p}} \right)\quad \sqrt{D^{2} - r^{2}}}}{D^{2}}$

The second line is defined as follows:$a = \frac{{r\left( {x_{c} - x_{p}} \right)} - {\left( {y_{c} - y_{p}} \right)\quad \sqrt{D^{2} - r^{2}}}}{D^{2}}$$b = \frac{{r\left( {y_{c} - y_{p}} \right)} + {\left( {x_{c} - x_{p}} \right)\quad \sqrt{D^{2} - r^{2}}}}{D^{2}}$

Those skilled in the art should recognize that the measurement method ofthis invention can include other two dimensional measurements and themethod can be generalized to three dimensional or higher dimensionalmeasurements of geometric entities.

The invention has been described herein in considerable detail in orderto comply with the Patent Statutes and to provide those skilled in theart with the information needed to apply the novel principles and toconstruct and use such specialized components as are required. However,it is to be understood that the inventions can be carried out byspecifically different equipment and devices, and that variousmodifications, both as to the equipment details and operatingprocedures, can be accomplished without departing from the scope of theinvention itself.

What is claimed is:
 1. A structure-guided image estimation methodcomprising the steps of: a) receiving a measurement mask; b) receiving ameasurement weight image; c) Inputting at least one structureconstraint; d) Performing at least one estimation from the weight imagewithin the region defined by the measurement mask using the at least onestructure constraint and e) generate a symbolic representation output ofa geometric entity.
 2. The method of claim 1 further comprises astructure-guided measurement step.
 3. The method of claim 1 furthercomprises a measurement mask generation step.
 4. The system of claim 1further comprises a measurement weight generation step.
 5. Astructure-guided estimation method comprising the steps of: a) inputtingat least one symbolic representation of a geometric entity; b) inputtingat least one structure constraint; c) performing parameter estimation ofthe symbolic representation using the at least one structure constraint.6. The method of claim 5 wherein the symbolic representation of ageometric entity includes a point.
 7. The method of claim 5 wherein thesymbolic representation of a geometric entity includes a line.
 8. Themethod of claim 5 wherein the symbolic representation of a geometricentity includes a circle.
 9. The method of claim 5 wherein the parameterestimation includes a line estimation.
 10. The method of claim 5 whereinthe parameter estimation includes a circle estimation.
 11. The method ofclaim 5 wherein the parameter estimation includes a circular arcestimation.
 12. A robust weight estimation method comprising the stepsof: a) receiving a plurality of learning images; b) performing referencelearning to generate reference weights; c) receiving a measured weightimage; d) combining the reference weight and measured weight images toproduce an output weight image.
 13. A robust estimation methodcomprising the steps of: a) receiving a measurement weight image; b)performing an initial estimate for an image feature; c) generatingreliability scores from the measurement weight image and the initialestimate; d) updating the weight image using the reliability score; e)updating the initial estimate using the updated weight image.
 14. Astructure-guided measurement method comprising the step of: a) inputtingat least one symbolic representation of a geometric entity; b) inputtingat least one structure constraint; c) applying at least one measurementof the symbolic representation using the at least one structureconstraint and d) generate at least one measurement output.
 15. Themethod of claim 14 wherein the measurement includes the determination ofan intersection point.
 16. The method of claim 14 wherein themeasurement includes the determination of an angle.
 17. The method ofclaim 14 wherein the measurement includes the determination of thedistance between a point and a line.
 18. The method of claim 14 whereinthe measurement includes the determination of the distance between twolines.
 19. The method of claim 14 wherein the measurement includes thedetermination of the tangential line of a circle.
 20. The method ofclaim 14 wherein the measurement includes the relative positions betweentwo or more geometric entities.